The situation is simplified. I want to explore a here - and want to know whether white can live locally, in the game black was so strong outside that establishing a running group won't help.
hhw: Black can certainly stop White from getting the corner. Unless Black completely dominate the part of the board we don't see (like what tapir implies), the marked stone may come under pressure if Black plays this way.
Dieter: With low, should explore life on the left side.
hhw: Checking joseki gives this. After , Black a, White throws in at b for ko. Joseki includes a push by White at c, Black can answer d here and give White another ko threat.